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A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

The norm topology on a normed space X=(X,||·||_X) is the topology tau consisting of all sets which can be written as a (possibly empty) union of sets of the form B_r(x)={y in ...

The theory and applications of Laplace transforms and other integral transforms.

An outcome is a subset of a probability space. Experimental outcomes are not uniquely determined from the description of an experiment, and must be agreed upon to avoid ...

Let {y^k} be a set of orthonormal vectors with k=1, 2, ..., K, such that the inner product (y^k,y^k)=1. Then set x=sum_(k=1)^Ku_ky^k (1) so that for any square matrix A for ...

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

A triple (S,S,P) on the domain S, where (S,S) is a measurable space, S are the measurable subsets of S, and P is a measure on S with P(S)=1.

For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

The second-order ordinary differential equation y^('')=y^(3/2)x^(-1/2).